Question

Suppose that a friend of yours (named Muriel) from Britain claims to be able to tell by tasting whether if the milk was added before the brewed tea when preparing a cup of tea.

To check this claim, you've prepared 10 cups of tea of which some have milk added first and others have milk added last. For each tea, Muriel will guess whether the milk was added first or last.

Now, we are going to assume that your friend does NOT actually have the skill to tell whether milk was added first or last (meaning that her guess is random). Let X=number of correct guesses from 10 cups of tea tasting.

Find the probability that she guesses at least 6 correctly.

• 0.1776

• 0.3770

• 0.8332

• 0.2051

Answer 1

If her guesses are random then we can model this problem using a Binomial distribution.

Muriel tastes 10 cups of tea, so no of trials is 10. Let p denote the probability of her guessing that milk was added first. Then, given she guesses randomly, p=0.5.

Every trial, that is the act of guessing, is independent of each other. Hence, X~Bin(10,0.5)

The pdf of X:

             

Thus, the probability that she guesses at least 6 correctly is:

  

Therefore,

The required probability is 0.3770